The ${\mathrm{K}}_{\mathrm{a}}$of hydrocyanic acid, HCN, is $5.0\times {10}^{-10}$ What is the pH of $0.050\mathrm{MHCN}\left(aq\right)$?

in case of weak acid 

$\begin{array}{l}\left[H^{+}\right]=\sqrt{\mathrm{Ka}\cdot \underset{\_}{C}}\\ \left[{\mathrm{H}}^{+}\right]=\sqrt{5\times {10}^{-10}\times 50\times {10}^{-3}}\\ =\sqrt{5\times 5\times {10}^{-12}}\\ =5\times {10}^{-6}\end{array}$

$\begin{array}{r}{P}^H=-\log \left[{\mathrm{H}}^{+}\right]\\ =-\log \left(5\times {10}^{-6}\right)\end{array}$

$=6-\log 5=6-0.67=5.33$